## 141 Citations

Notes on Gorenstein Flat Modules

- MathematicsBulletin of the Iranian Mathematical Society
- 2018

In this paper, we explore conditions under which Gorenstein flat modules are Gorenstein projective. We prove that all countably presented strongly Gorenstein flat modules are Gorenstein projective…

When Every Gorenstein Projective (Resp. Flat) Module is Strongly Gorenstein Projective (Resp. Flat)

- MathematicsCommunications in Mathematics and Applications
- 2010

In [5], the authors discuss the rings over which all modules are strongly Gorenstein projective. In this paper, we are interesting to an extension of this idea. Thus, we discuss the rings over which…

n -Strongly Gorenstein Projective and Injective Complexes

- Mathematics
- 2016

In this paper, we introduce and study the notions of n-strongly Gorenstein projective and injective complexes, which are generalizations of n-strongly Gorenstein projective and injective modules,…

A Characterization of Gorenstein Projective Modules

- Mathematics
- 2016

In this article, we give a new characterization of Gorenstein projective modules. As applications of our result, we prove that a strongly Gorenstein projective module of countable type is Gorenstein…

Gorenstein FC-projective modules

- Mathematics, PhysicsJournal of Algebra and Its Applications
- 2019

In this paper, we investigate Gorenstein FC-projective modules and Gorenstein FC-projective dimensions, and characterize rings over which every module is Gorenstein FC-projective and rings over which…

STRONGLY GORENSTEIN FLAT MODULES

- MathematicsJournal of the Australian Mathematical Society
- 2009

Abstract In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-module M is called strongly Gorenstein flat if there is an exact sequence ⋯→P1→P0→P0→P1→⋯ of projective…

On Strongly Gorenstein FP-Injective Modules

- Mathematics
- 2013

This article continues to investigate a particular case of Gorenstein FP-injective modules, called strongly Gorenstein FP-injective modules. Some examples are given to show that strongly Gorenstein…

Strongly Gorenstein flat and Gorenstein FP-injective modules

- Mathematics
- 2013

In this paper, we first study the properties of strongly Gorenstein flat (resp. Gorenstein FP-injective) modules which are special Gorenstein projective (resp. Gorenstein injective) modules, and use…

(n, m)-Strongly Gorenstein Projective, Injective and Flat Modules

- Mathematics
- 2011

Some properties of -Strongly Gorenstein projective ,injective and flat modules are studied and some connections between -Strongly Gorenstein projective , injective and flat modules are discussed . At…

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- Mathematics
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- Mathematics
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In order to research the structure and properties of modulcs overings and algebras,In this paper,by using homological methods we investigated the ralation between Gorenstein injective modules and…

Relative homological coalgebras

- Mathematics
- 2004

We study classes of relative injective and projective comodules and extend well-known results about projective comodules given in [7]. The existence of covers and envelopes by these classes of…

Foxby duality and Gorenstein injective and projective modules

- Mathematics
- 1996

In 1966, Auslander introduced the notion of the G-dimension of a finitely generated module over a Cohen-Macaulay noetherian ring and found the basic properties of these dimensions. His results were…

On finitely generated flat modules

- Mathematics
- 1969

Introduction. The aim of this paper is to study conditions which reflect the projectivity of a given finitely generated flat module over a commutative ring. The use of the invariant factors of a…

Finitely Generated Flat Modules and a Characterization of Semiperfect Rings

- Mathematics
- 2003

Abstract For a ring S, let K 0(FGFl(S)) and K 0(FGPr(S)) denote the Grothendieck groups of the category of all finitely generated flat S-modules and the category of all finitely generated projective…

Absolute, Relative, and Tate Cohomology of Modules of Finite Gorenstein Dimension

- Mathematics
- 2002

We study finitely generated modules M over a ring R, noetherian on both sides. If M has finite Gorenstein dimension G‐dimRM in the sense of Auslander and Bridger, then it determines two other…

An introduction to homological algebra

- Mathematics
- 1960

Preface 1. Generalities concerning modules 2. Tensor products and groups of homomorphisms 3. Categories and functors 4. Homology functors 5. Projective and injective modules 6. Derived functors 7.…

Flat covers of modules

- Mathematics
- 1996

Envelopes and covers.- Fundamental theorems.- Flat covers and cotorsion envelopes.- Flat covers over commutative rings.- Applications in commutative rings.